How do you find the equation of a parabola given endpoints of latus rectum?

use h, k, and p to find the coordinates of the focus, (h+p,k) use h andp p to find the equation of the directrix, x=h−p. use h, k, and p to find the endpoints of the latus rectum, (h+p,k±2p)

How do you find the equation of a parabola given the endpoints?

use h,k , and p to find the coordinates of the focus, (h, k+p) use k and p to find the equation of the directrix, y=k−p. use h,k , and p to find the endpoints of the focal diameter, (h±2p, k+p)

How do you find the Latus of a parabola?

The length of the parabola ‘s latus rectum is equal to four times the focal length. In an ellipse , it is twice the square of the length of the conjugate (minor) axis divided by the length of the transverse (major) axis. In a circle , the latus rectum is always the length of the diameter .

What is end point of latus rectum?

The line segment that passes through the focus and is parallel to the directrix is called the latus rectum. The endpoints of the latus rectum lie on the curve. By definition, the distance d from the focus to any point P on the parabola is equal to the distance from P to the directrix.

How do you measure latus rectum?

The length of the latus rectum in a parabola is equal to the four times the focal length. The length of the latus rectum in hyperbola is equal to twice the square of the length of the transverse axis divided by the length of the conjugate axis.

What does Latus mean?

The section of flesh on the body of a person or an animal between the last rib and the hip; the side. 2. A cut of meat from the flank of an animal. 3. A lateral part or side: the flank of a mountain.

What are the end points of latus rectum of the parabola y 2 16x?

Solution: The given equation of the parabola y2 = 16x can be compared with the standard equation of the parabola y2= 4ax. Hence we have 4a = 16, and 1 = 4. Therefore, the length of the latus rectum is 16, and the ends of the latus rectum is (4, 8), and (4, -8).

How do you find the endpoints of latus rectum in a hyperbola?

Latus rectum of a hyperbola is defined analogously as in the case of parabola and ellipse. The ends of the latus rectum of a hyperbola are (ae, ±b2/a2), and the length of the latus rectum is 2b2/a.

How do you find the end of latus rectum of a hyperbola?

The length of the latus rectum in hyperbola is equal to twice the square of the length of the transverse axis divided by the length of the conjugate axis….

Conic Section	Length of the Latus Rectum	End of the Latus Rectum
y²= 4ax	4a	L= ( a, 2a) , L’ (a, -2a)

How to find the length of the latus rectum of a parabola?

Find the length of the latus rectum whose parabola equation is given as, y 2 = 12x. Since y 2 = 4ax is the equation of parabola, we get value of a: Hence, the length of the latus rectum of a parabola is = 4a = 4 (3) =12. Find the length of the latus rectum of an ellipse 4x 2 + 9y 2 – 24x + 36y – 72 = 0.

How do you find the equation of a parabola?

Given latus rectum joining the points (4, 6) and (4, -2). Equation of parabola is y 2 = 4ax. y 2 = 8x is the required equation. Example 2. Find the equation of the parabola whose focus is at (3,0) and the length of the latus rectum is 12. y 2 = 12x is the required equation.

How do you find the focus of a parabola?

Parabola Equation 1 Focus: The point (a, 0) is the focus of the parabola 2 Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. 3 Focal Chord: The focal chord of a parabola is the chord passing through the focus of the parabola.

What is half of the latus rectum called?

Half the latus rectum is called the semi latus rectum. The diagram above shows the latus rectum of a parabola. Let the ends of the latus rectum of the parabola, y 2 =4ax be L and L’.